Corresponding author: C. M. Poindexter, Department of Civil and Environmental Engineering, University of California, Berkeley, 750 Davis Hall, Berkeley, CA 94720-1710, USA. (cpoindexter@berkeley.edu)

Abstract

[1] Methane, carbon dioxide, and oxygen are exchanged between wetlands and the atmosphere through multiple pathways. One of these pathways, the hydrodynamic transport of dissolved gas through the surface water, is often underestimated in importance. We constructed a model wetland in the laboratory with artificial emergent plants to investigate the mechanisms and magnitude of this transport. We measured gas transfer velocities, which characterize the near-surface stirring driving air-water gas transfer, while varying two stirring processes important to gas exchange in other aquatic environments: wind and thermal convection. To isolate the effects of thermal convection, we identified a semiempirical model for the gas transfer velocity as a function of surface heat loss. The laboratory results indicate that thermal convection will be the dominant mechanism of air-water gas exchange in marshes with emergent vegetation. Thermal convection yielded peak gas transfer velocities of 1 cm h^{−1}. Because of the sheltering of the water surface by emergent vegetation, gas transfer velocities for wind-driven stirring alone are likely to exceed this value only in extreme cases.

[2] Wetlands are a potentially sizable sink of atmospheric carbon dioxide but also emit more methane than any other source [Denman et al., 2007]. The net fluxes of both these gases in wetlands are sensitive to the availability of oxygen [e.g., Zhang et al., 2002]. Gas fluxes to and from the atmosphere in wetlands can occur via three pathways: the gas-filled tissue or aerenchyma of emergent vegetation, bubbles rising from the substrate to the water surface (ebullition), and hydrodynamic transport of dissolved gas through the surface water. Our focus is on the last of these. While the other pathways may dominate at times, hydrodynamic transport of dissolved gas is particularly important when emergent vegetation is senescent; it may also indirectly reduce transport via the other two pathways, like plant-mediated transport reduces ebullition [Bazhin, 2004], since the stocks of dissolved gas in the wetland from which the three different pathways convey gas are hydraulically linked.

[3] Hydrodynamic gas transport has received notably little study so far, and we present below the first detailed mechanistic exploration of this pathway in wetlands. A central goal is to help those evaluating wetland greenhouse gas fluxes, either via biogeochemical models or observation, accurately capture hydrodynamically driven gas fluxes.

2 Background

[4] Hydrodynamically driven gas flux (J) across the air-water interface can often be modeled as the product of a gas transfer velocity (k) and the difference between the dissolved gas concentration at the water surface (C_{eq}), which is in equilibrium with the air above, and the concentration in the bulk of the water column (C).

J=kCeq−C(1)

[5] The gas transfer velocity k is a measure of the near-surface stirring in the water that drives exchange of sparingly soluble gases across the air-water interface. As we will show later, this model is appropriate even in wetlands with relatively slow-moving water. In the convention of gas transfer literature, k is normalized to k_{600}. k_{600} is the equivalent gas transfer velocity for CO_{2} gas at 20°C, which has a Schmidt number (Sc) of 600. This normalization allows measurements of k made using one gas to be used with other gases and is shown in equation (2), where n is a factor characterizing the kinematic behavior of the water surface.

k600=k600Sc−n(2)

[6] A long-standing challenge is finding k values that accurately describe the different stirring forces found in environmental flows. Some models for k directly represent the near-surface hydrodynamics, such as the surface divergence [Turney et al., 2005] or the surface dissipation rate of turbulent kinetic energy [Zappa et al., 2007], and thus are most broadly applicable. Empirical models for the gas transfer velocity give k as a function of an easily measured variable that characterizes the most important stirring force. In nonfluvial systems, this force is often the wind.

[7] The gas transfer velocity in the ocean has been found to vary with the square of the wind speed 10 m above the water surface U_{10} [Wanninkhof, 1992]. In sheltered inland waters with lower wind speeds and fetch, empirical models have been proposed in which the dependence on wind speed is modified and the gas transfer velocity is nonzero at zero wind speeds [e.g., Sebacher et al., 1983; Cole and Caraco, 1998; Crusius and Wanninkhof, 2003]. The nonzero intercept in these models may represent the effects of thermal convection, which occurs when the water surface loses heat. Indeed, there is increasing evidence that thermal convection plays a key role in gas transfer at low wind speed in lakes and the ocean [Schladow et al., 2002; Eugster et al., 2003; McGillis et al., 2004; Read et al., 2012], and it has recently been given a more explicit treatment in gas transfer models. For example, MacIntyre et al. [2010] model k with two functions of U_{10}, one for periods of surface heat loss and another for periods of heat gain. Another model addresses the combined effects of surface heat loss and wind on air-water gas transfer via the surface dissipation of turbulent kinetic energy [Soloviev et al., 2007]. In this model, three sources of turbulent kinetic energy in the ocean—buoyancy, wind shear, and wave breaking—figure into the calculation of surface dissipation. k is proportional to the heat loss to the one-fourth power in the limit of calm winds and a function of the shear velocity in the atmospheric boundary layer at higher wind speeds.

[8] It is not clear that the same models used for k in oceans, lakes, and ponds can be directly applied to wetlands with emergent vegetation. This is because emergent vegetation will attenuate wind speed above the water surface, modify fluid shear at the water surface, and influence stirring beneath the water surface [Raupach et al., 1996; Nepf et al., 1997]. Emergent vegetation will also damp waves [Augustin et al., 2009], moderate the heating and cooling of the water column [Burba et al., 1999a], and even stir the water column via “honami” waving.

[9] Some existing results allow us to estimate the effect of these factors. Measurements in forests and agricultural crops [Raupach et al., 1996] show a rapid loss of wind speed (up to 90% reduction) through the top of the vegetation, which suggests that surface wind shear will play a reduced role in driving gas transfer in wetlands with emergent vegetation. Vegetation stems can contribute to turbulent kinetic energy through wake production [Nepf et al., 1997], potentially enhancing gas transfer. Nighttime heat losses in open water can exceed heat losses in emergent vegetation by a factor of 5 [Burba et al., 1999a], which raises the possibility that thermal convection and resulting gas transfer may be less intense in wetlands than in areas of open water.

[10] There are few data sets to test these hypotheses or predict k for wetlands specifically [Kadlec and Wallace, 2009; Kadlec and Knight, 1996].The handful of gas transfer velocity measurements that have been made in wetlands with emergent vegetation show that k values are an order of magnitude lower than those commonly measured in the ocean, lakes, or rivers. Specifically, floating chamber measurements in a Florida hardwood swamp indicated that k_{600} averaged 0.78 ± 0.54 cm h^{−1} [Happell et al., 1995], and SF_{6} tracer releases in the patterned marshes of the Florida Everglades indicated k_{600} there ranged from 0.3 to 1.8 cm h^{−1} [Variano et al., 2009]. While these observed values in wetlands are quite low, they are still too large to represent the effects of molecular diffusion alone.

[11] Since gas transfer velocities in wetlands with emergent vegetation differ from those in other aquatic environments, and emergent vegetation modifies the common drivers of gas transfer in various ways, wetland-specific data are needed. Ideally, these measurements would isolate each of the stirring forces influencing gas transfer. A number of stirring processes from current to rainfall to seiches may affect gas transfer in wetlands. Here we focus on how k in wetlands with emergent vegetation varies with two common drivers of gas transfer: thermal convection and wind shear at the air-water interface. We parameterize thermal convection with the surface heat loss q. We parameterize the effects of wind with the mean wind speed in the constant velocity or shear-free region of the vegetation canopy, which we call <U_{canopy}>. The constant velocity region occurs deep in the canopy, below the region where the mean wind speed decays rapidly with height [Massman, 1987; Katul et al., 2004; Ghisalberti and Nepf, 2004].

[12] Using a laboratory model wetland, we measure k for a range of surface heat flux and <U_{canopy}> values, which were selected based on measurements of meteorological conditions in real wetlands, including our own field measurements of U_{canopy}. We also use an analytical approach to quantify the effect of thermal convection on air-water gas transfer. Because surfactants are often present in natural waters and they affect gas transfer by reducing surface divergence [McKenna and McGillis, 2004], we account for surfactants in both our analytical and experimental work. The largest-scale eddies in the canopy wind field are highly intermittent [Raupach et al., 1996; Finnigan, 2000]; hence, we explore the need for an additional factor beyond the mean wind speed <U_{canopy}> to characterize the effect of wind on k. In addition, we examine the flows around emergent plant stems to assess the stems' contribution to the near-surface hydrodynamics directly responsible for gas transfer.

3 Methods

[13] We designed the model wetland in the laboratory (Figure 1) to replicate the length and velocity scales in natural wetlands. The model wetland consists of a tank—4 m long, 0.8 m wide, and 1 m high—to which water can be added to a maximum height of 0.5 m. Above this height, the tank is open at each end, creating a wind tunnel atop the water column. Approximately 500 (1 m long, 13 mm diameter) rigid plastic tubes are spaced randomly throughout the tank. Their circular cross sections mimic emergent stems, most notably Schoenoplectus acutus, commonly known as tule or bulrush. The tubes extend from the bottom of the water column to the top of the wind tunnel and are held in place so they do not move during experiments. Artificial plants suffice for our model wetland because our concern is not plant-mediated gas transport but the effect of emergent wetland plants on hydrodynamic transport through the water column and air-water interface.

[14] The stem density in the model wetland, 158 stems per m^{2}, falls within the range of mean stem densities reported for S. acutus and Schoenoplectus californicus across several real wetlands: 83–331 stems per m^{2} [Miller and Fujii, 2010; Sartoris et al., 2000; Gardner et al., 2001]. Assuming a stem diameter of 13 mm (the one mean stem diameter reported among these real wetlands [Gardner et al., 2001]), this range of stem densities corresponds to plant volume fractions from 0.011 to 0.042. We use ϕ = 0.02 in the model wetland and evaluate how the results may vary for other values of ϕ in section 5.5.

[15] We conducted experiments in the model wetland at wind speeds of 0.05 to 1.1 m s^{−1}, using an adjustable main fan to control speeds and an array of programmable small fans to condition the air flow. The relationship between these speeds and those found in the field is discussed in section 4.1. We measured wind speed <U_{canopy}> in the laboratory with a sonic anemometer (Campbell Scientific CSAT3) located 0.4 m above the water column and within the canopy of emergent “stems.” Uncertainty in <U_{canopy}> values is equal to the sum of several possible sources of error in quadrature including sonic anemometer offset uncertainty and error due to possible anemometer misalignment with the tunnel axes.

[16] We varied surface heat fluxes from −310 to 140 W m^{−2}, where a negative heat flux indicates a cooling water column. This range overlaps with the range measured in studies in temperate wetlands in California, Oregon, Nebraska, and Indiana: −200 and +300 W m^{−2} [Drexler et al., 2008; Bidlake, 2000; Burba et al., 1999b; Souch et al., 1996]. In these natural wetlands, heat fluxes followed the diurnal pattern of solar radiation. Daytime radiative and sensible heating caused net positive heat flux, while radiative cooling, sensible heat loss, and evaporation caused negative heat flux at night. In our model wetland, we varied q between experiments by varying the initial bulk water temperature in the tank. Natural variations in the ambient air temperature and humidity also affected surface heat fluxes. We account for these factors and all forms of surface heat loss in the calculation of q. Closed cell foam and double-paned plexiglass insulated the tank walls, reducing heat exchange through interfaces other than the water surface and permitting the calculation of surface heat flux q from the change in the bulk water temperature over time:

q=dTbdtρcpH(3)

where c_{p} is the isobaric heat capacity, ρ is the water density, H is the depth of the water column, and T_{b} is the bulk water temperature. We measured temperature at mid-depth using our dissolved oxygen meter (discussed below) and calculated dTbdt from a linear regression of temperature readings during each experiment.

[17] To control surfactant concentration, we filled the water basin to 45 cm before the start of an experiment and then skimmed and discarded the top 5 cm of the water column. Particle image velocimetry (discussed in section 5.5) confirmed that surface skimming qualitatively changed the character of the near-surface flow, in a manner consistent with cleaner surface conditions. These data also indicated that clean conditions were maintained for at least 1 h following skimming.

[18] We measured k by monitoring the rate of increase of dissolved oxygen (DO) in the water column after chemically lowering the DO below the air-water equilibrium value. We monitored DO at 30 s intervals with an optical probe (YSI ProODO) placed at mid-depth in the water column near the center of the tank. The DO probe also sensed temperature and pressure, which we used along with Henry's law coefficients identified by Benson and Krause [1984] to calculate equilibrium DO (C_{eq}).

[19] Combining equation (1) and an oxygen mass balance for the tank and then integrating yields an equation for DO concentration as a function of time.

lnCeq−Ct=−kHt+lnCeq−C0(4)

H is the tank depth, C_{eq} is the DO concentration at the surface, C(t) is the DO concentration in the bulk (i.e., well mixed) region of the water column, and C_{0} is the initial value for C. It follows from this equation that ln (C_{eq}− C) varies linearly in time and that the slope of this line is −k/H. This solution applies only when C_{eq} (and thus temperature) is steady in time. Thus, we analyze our measurements in subsets of nearly constant temperature. We compute a gas transfer velocity k for each subset using equation (4), normalize each k value to k_{600}, and then take the median of these k_{600} values to obtain a single value of k_{600} for an individual experiment. When normalizing to k_{600} with equation (2), we specify n using the free-slip value of n = 1/2 when the air-water interface was skimmed to remove surfactants prior to an experiment and the no-slip value n = 2/3 when the surface was not skimmed.

[20] We validate our approach to hydrodynamic gas transport in wetlands by measuring the profile of DO in the water column. There are two common approaches to diffusive transport near an interface. The first assumes that diffusivity increases continuously with distance from the interface. The second assumes two regions of different diffusivities: a region adjacent to the interface with small diffusivity and a well-mixed bulk region far from the interface with infinite diffusivity. The latter model is often preferred due to its simplicity and allows for the definition of a gas transfer velocity k ≡ J/(C_{eq} − C) as in equation (1). The two models lead to different concentration profiles given the same initial and boundary conditions. In our experimental setup, we expect to see a nearly uniform concentration in the bulk if k is a valid parameterization of gas transfer. DO profiles measured after more than 1 h of wind tunnel operation with mean canopy wind velocities between 0.5 and 1.1 m s^{−1} are plotted in Figure 2 and show a well-mixed bulk with constant DO, validating the use of k to parameterize gas transfer.

4 Results

4.1 Validation of Model Wetland Wind Conditions

[21] Predicting <U_{canopy}> from more commonly measured wind parameters is nontrivial, though in crop canopies, it has been found to scale with the shear velocity when the atmospheric boundary layer is neutral or unstable [Jacobs et al., 1995]. To our knowledge, no measurements of in-canopy wind speed have been made in natural wetland canopies, so we conducted field studies to determine the relevant range of <U_{canopy}> in wetlands. We measured the horizontal wind speed profile within the 2.5 m tall emergent vegetation canopy of an enclosed 3 ha wetland on Twitchell Island in the Sacramento-San Joaquin Delta (Northern California, USA). Typha spp. (cattail) and S. acutus are the dominant emergent vegetation species, and they cover more than 95% of the wetland area [Miller and Fujii, 2010]. We measured wind speeds with a sonic anemometer, profiling heights from 25 cm to 2 m above the water surface for a minimum of 10 min at each height. Because wind speed measurements at different heights were made sequentially over several hours, we normalized the data by the wind speed at a height of 2 m (U_{2}) measured at a nearby California Irrigation Management Information System weather station (http://wwwcimis.water.ca.gov/). We collected one profile on a day when mean wind speed at the nearby weather station was 4.1 m s^{−1}, close to the annual average, and a second on a calm day, both in October 2011.

[22] The wind speed profiles are shown in Figure 3 and indicate a nearly shear-free layer in the canopy near the water surface. In this shear-free layer, <U_{canopy}> ≈ 0.1 m s^{−1} on the day with calm wind and <U_{canopy}> ≈ 0.3 m s^{−1} on the day with average above-canopy wind. In-canopy winds gusted up to 1.7 m s^{−1} on the windier day. Laboratory wind tunnel airflows were also uniform over z, as shown in three laboratory-measured velocity profiles in Figure 3. The range of wind speeds we use in the laboratory covers the range of wind speeds found in the field, in terms of both 10 min average wind speeds and gusts.

4.2 Model Wetland Results

[23] Laboratory results for k are shown in Figure 4 as a function of <U_{canopy}> and q. Circles represent those measurements preceded by surface skimming to obtain a repeatable level of surface cleanliness. For the skimmed cases and <U_{canopy}> greater than 0.9 m s^{−1}, the results are closely clustered at approximately 3 cm h^{−1}. In one notable exception with strong negative heat flux (q < −200 W m^{−2}), k_{600} was 5.1 cm h^{−1}, indicating the importance of thermal convection, in addition to wind speed. For <U_{canopy}> greater than 0.9 m s^{−1}, omitting the skimming step prior to measurement resulted in greater spread in the k_{600} data as well as a lower median value of k_{600} (2.3 versus 3.0 cm h^{−1}).

[24] For <U_{canopy}> less than 0.7 m s^{−1}, there is no discernible trend between <U_{canopy}> and k_{600}. Instead, k_{600} appears to increase as heat flux becomes negative and drops further below zero. The lowest value of k_{600} occurs when heat flux is positive (q = 46 W m^{−2}). To investigate the role heat flux played on gas transfer in the model wetland, we identify an analytical relationship between q and k.

5 Analysis and Discussion

5.1 Analytical Model for k Versus q

[25] Sufficient conditions for convective mixing occur when the water is losing heat to the air (q < 0). The heat transfer velocity k_{h} is analogous to the gas transfer velocity. As in equation (2), using the Prandtl number Pr (for heat) and a Schmidt number of 600 (for mass), we can scale the heat transfer velocity k_{h} to the mass transfer velocity k_{600}.

k600=kh600Pr−n(5)

[26] Via the next series of equations, we identify a semiempirical relationship for the heat transfer velocity and then apply equation (5) to obtain an equation for the gas transfer velocity. The Nusselt number is the ratio of the total heat transfer to the heat transfer by molecular diffusion alone:

Nu=khLα(6)

α is the thermal diffusivity and L a length scale that drops out later. When the additional heat transfer beyond molecular diffusion is due to stirring by thermal convective motions, we can find Nu from a semiempirical relationship of the Rayleigh number (Ra_{T}). For high Rayleigh number flow (Ra_{T} > 8 × 10^{6}) below a cold horizontal boundary,

Nu=0.14RaT1/3±7%(7)

[Martynenko and Khramtsov, 2005]. While Ra_{T} is defined in terms of a temperature difference, there is also a flux Rayleigh number Ra_{q} that is a function of heat flux q:

Raq=−qgBL4α2νcpρforq<0(8)

where B is the thermal expansion coefficient, g is the gravitational acceleration, and ν is the kinematic viscosity. The two Rayleigh numbers are related through the Nusselt number [Bejan, 1995].

RaT=RaqNu(9)

[27] Combining equations (6)–(9), we obtain an expression for the heat transfer velocity. Applying the scaling relationship in equation (5) yields an expression for the gas transfer velocity.

[28] This analysis indicates that the gas transfer velocity for thermal convection is proportional to the heat loss, −q, to the one-fourth power. This relationship holds for negative flux values (heat loss) only and for a minimum level of thermal convection (Ra_{T} > 8 × 10^{6}). Using the wetland depth as the length scale L, we calculate that the Rayleigh number threshold for equation (10) is met for wetland water columns deeper than 10 cm for typical heat loss rates.

[29] The uncertainty in equation (10) is dominated by the reported 7% uncertainty in equation (7) and a 10% error in equation (2) when n is known to within 0.02 [Jähne and Haußecker, 1998]. A key assumption in this treatment of convective interfacial flux is that vegetation stems rising through the water column have negligible effect on thermal convection. Numerical simulations have shown that the characteristic horizontal length scale of convection cells at a free surface is on the order of 5 cm for a heat flux of −100 W m^{−2} [Leighton et al., 2003]. The characteristic interstem spacing in our laboratory experiment is 8 cm; thus, the presence of stems should not interfere with convective motions. It is not until vegetation densities of ϕ >≈ 6% that the interstem spacing is similar to the size of convection cells.

[30] Equation (10) for k_{600} versus q is similar to that derived by Soloviev et al. [2007] using a different approach, namely the calculation of turbulent kinetic energy dissipation from buoyancy flux and calculation of k from dissipation. Soloviev et al. [2007] use a value of 0.25^{3/4} for the coefficient rather than 0.14^{3/4}, which results in k_{600} values approximately 50% higher than those derived from equation (10) for n = 1/2.

5.2 Coupled and Independent Effects of Wind Shear and Thermal Convection

[31] We calculate using equation (10) the value of k_{600} that would be expected if all observed interfacial gas fluxes in the model wetland were caused by thermal convection alone. The amount by which observed k_{600} values exceed this prediction is an indication of how much wind stirring enhances k_{600}. This difference can be seen in Figure 5 by comparing observations (points) to model predictions (lines). The two model lines correspond to the end-member cases of surface cleanliness: n = 1/2 and n = 2/3.

[32] We first consider gas transfer velocities measured at the highest canopy wind speed (0.9–1.1 m s^{−1}), shown in charcoal gray in Figure 5. For the three measured k_{600} values to the right of the origin, where we know convection is not contributing to gas transfer because the water column is gaining heat (q > 0), there is a consistent value of k_{600} of approximately 3 cm h^{−1}. We take 3 cm h^{−1} as the independent value of interfacial transport by wind at <U_{canopy}> ≈ 1 m s^{−1}.

[33] Except for one data point, observed k_{600} values at <U_{canopy}> greater than 0.9 m s^{−1} are also approximately 3 cm h^{−1} on the left side of the origin where heat flux is negative. These k_{600} values are each less than the sum of k_{600} predicted from heat flux and the independent value of k_{600} for wind-driven stirring alone. Wind shear apparently overwhelms the effects of increasing surface heat loss when <U_{canopy}> is greater than 0.9 m s^{−1} and q > −200 W m^{−2}. For the measurement in which q = −310 W m^{−2}, the observed k_{600} is equal to the value predicted from the heat flux (2 cm h^{−1}) plus the independent value of k_{600} for wind alone (3 cm h^{−1}).

[34] All observed k_{600} values measured with <U_{canopy}> less than 0.7 m s^{−1} and q < 0, shown as white markers in Figure 5, fall between the upper and lower uncertainty bounds for k_{600} predictions due to thermal convection alone. This suggests that when wind speeds are low and q is less than zero, q alone determines k_{600}. When wind speeds are low and q is greater than zero, we find that k_{600} is very small but nonzero. Specifically, at a wind speed of 0.3 m s^{−1} and q = 46 W m^{−2}, we measured the lowest gas transfer velocity in this study, k_{600} = 0.11 cm h^{−1}.

[35] From the above analyses, we conclude that wind-driven mixing alone was responsible for the gas transfer velocities of 2.6–3.3 cm h^{−1} measured at a <U_{canopy}> of 0.9–1.1 m s^{−1} as well as the gas transfer velocity of 0.11 cm h^{−1} measured at a <U_{canopy}> of 0.3 m s^{−1}. These conclusions suggest that k_{600} due to wind alone can be modeled as a nonlinear function passing through the origin (for surfactant-free surfaces): k_{600} = A<U_{canopy}>^{2} where A ≈ 3 cm h^{−1} m^{−2} s^{2}. We choose to use a quadratic function in analogy with the results of Wanninkhof [1992] for much higher wind speeds in the ocean. Other functional forms are possible and the fit would benefit from more data, but this approximate result is sufficient for the remainder of our analysis.

5.3 Implications for Wetland Gas Fluxes

[36] Field measurements suggest that it is very rare for <U_{canopy}> to exceed 0.7 m s^{−1} but that q can reach −200 W m^{−2} in wetlands. Thus, thermal convection will typically dominate wind shear in setting k_{600} in wetlands with emergent vegetation. In contrast, the wind is the dominant factor determining k in oceans. Lakes fall in the regime between wetlands and oceans, with both wind shear and surface heat loss driving gas transfer, and the relative importance of these two forcings set by lake area. In a study of 40 lakes, thermal convection was estimated to drive no more than 21% of the total gas transfer in large lakes, while in small lakes, up to 79% of the total gas transfer was due to thermal convection [Read et al., 2012]. The increased importance of convection in small lakes is attributed to the increased topographic sheltering around these lakes [Read et al., 2012]. Because emergent vegetation in wetlands shelters the water surface even more effectively than adjacent topography, it is logical that convection should dominate hydrodynamic transport in wetlands with emergent vegetation.

[37] The dominance of thermal convection suggests that the gas transfer velocity will exhibit a stronger diurnal variation in wetlands than in most lakes. This is because daytime values of k_{600} will drop during the day when q > 0 and then increase significantly at night when surface cooling yields thermal convection. Laboratory measurements suggest that the daily variation in k_{600} will be roughly an order of magnitude, from k_{600} ≈ 0.1 cm h^{−1} to k_{600} ≈ 1 cm h^{−1}.

[38] Equation (10) was derived in a way that should apply to natural wetlands. Thus, we can apply this equation to predict k_{600} values and air-water gas transfer in natural wetlands, assuming that no other forcing (wind, rain, current, waves, etc.) is significant. The strongest cooling heat flux typically observed in wetlands is −200 W m^{−2}, causing a maximum k_{600} between 1 and 2 cm h^{−1} depending on the value of the exponent n. For wetland air-water interfaces, n falls between 1/2 and 2/3. Biological activity provides a significant source of surfactant contamination, which increases n toward 2/3. While surfactants increase n toward 2/3, n can also be lowered toward 1/2 by dilational surface flows that disrupt the surfactant layer [Jähne et al., 1987]. In wind-driven currents, persistent dilational regions form adjacent to plant stems (as we will show in section 5.5). If we assume conservatively that n = 2/3, equation (10) predicts that the typical nighttime k_{600} value will be 0.6 cm h^{−1}, based on a typical nighttime q value of −45 W m^{−2} (as measured in a Nebraska marsh [Burba et al., 1999a]). DO levels in emergent vegetation are often near zero [e.g., Rose and Crumpton, 1996], while the DO value in equilibrium with the atmosphere is approximately 10 g m^{−3} at 15°C. Assuming that respiration keeps DO near zero in the bulk of the water column, the total nighttime flux due to hydrodynamic transport is thus 1 g m^{−2}. As a point of comparison, this flux is the same order of magnitude as most estimates of daily plant-mediated oxygen flux in wetlands compiled by Kadlec and Knight [1996]. Some wetland biogeochemical models do not include the hydrodynamic transport of dissolved methane and/or oxygen, assuming that the other gas transport pathways dominate [Walter and Heimann, 2000; Potter, 1997; Cao et al., 1996; Zhang et al., 2002], but this sample calculation suggests otherwise, at least in the case of oxygen.

[39] On those rare occasions when strong winds cause shear-driven stirring of the water surface, our measurements suggest that k_{600} values will be roughly 5 times the typical nighttime value due to thermal convection alone. The factor of 5 is large, but not so large as to completely overwhelm the effects of daily average gas transfer. Thus, it is not clear whether overall gas transfer in wetlands is dominated by rare or average events. Future work could answer this question by considering the joint probability distribution of wind, heat flux, and dissolved gas concentration.

5.4 Accounting for Increased Wind Speed Variance in Real Emergent Plant Canopies

[40] The influence of extreme winds on k_{600} in wetlands suggests that we should consider the role of gusts, even when the time-averaged wind speed is small. Natural wind forcing varies over a wide range of timescales, and interactions between the wind and plant canopy generate intermittent, large-scale eddies [Raupach et al., 1996]. As a result, the variance of wetland in-canopy velocity is much greater in the field than in our laboratory model. For example, in the lab the fluctuation intensity, 〈(U_{canopy} − 〈U_{canopy}〉)^{2}〉^{1/2}/〈U_{canopy}〉, is 0.11 ± 0.01. At the wetlands on Twitchell Island in the Sacramento-San Joaquin Delta, the fluctuation intensity is 0.57 ± 0.05. This additional variance will affect k and can be expressed as an enhancement factor, as used, for example, by Wanninkhof et al. [2004] for wind in the ocean. We find the enhancement factor by conducting a Monte Carlo analysis using the approximate relationship: k600≈3Ucanopy2. When U_{canopy} has a stochastic distribution, then k600≈3Ucanopy2=3Ucanopy2β, where β is an enhancement factor. We can evaluate β by specifying a distribution of U_{canopy} values as the Monte Carlo model input.

[41] The predicted enhancement factors are not sensitive to either <U_{canopy}> or the kurtosis of the velocity distribution, both of which can vary significantly in environmental settings. The effect of velocity variance on β is shown in Figure 6, from which it is evident that a fluctuation intensity of 0.11, as measured in the lab, is essentially equivalent to a fluctuation intensity of 0. For a fluctuation intensity of 0.57 as observed at the wetlands on Twitchell Island, the enhancement factor is 1.3; hence, k_{600} values measured in the laboratory as a result of wind-induced stirring should be increased by 30% for these wetlands.

5.5 Applicability of Results to Different Plant Volume Fractions

[42] We employed vegetation with very specific characteristics in the model wetland, while in natural wetlands, vegetation density and diameter vary, both seasonally and spatially. We evaluate the applicability of our laboratory results to other plant volume fractions by considering the basic kinematics of near-surface stirring.

[43] For a wide variety of flows and surfactant levels, it has been shown that gas transfer velocity k scales with the expectation value of surface divergence magnitude |γ| to the one-half power [Turney et al., 2005; McKenna and McGillis, 2004]:

k=0.5νγSc−nwhereγ=∂u∂x+∂v∂yz=0(11)

Using equation (11) and velocity field measurements in the model wetland, we explore the relationship between k and plant volume fraction. With particle image velocimetry (PIV), we recorded time-varying water velocities u and v in a horizontal (x-y) plane near the air-water interface and used these data to compute surface divergence (e.g., Figure 7). The PIV optical setup included an Imager PRO-X camera with a 1600 × 1200 array of square pixels (actual size 7.4 µm) and a 532 nm dual Nd:YAG laser. The main body of Figure 7 shows time-averaged horizontal velocities and root divergence in a 5 cm × 5 cm region based on image pairs collected at 10 Hz for 18 s. At each time step, individual water velocity vectors were computed from an average of particle motion over regions having an area of 0.17 cm × 0.17 cm. The majority of measurements were collected while <U_{canopy}> ≈ 1 m s^{−1}, and we did not remove surfactants with skimming; thus, the character of wakes near the surface is affected by the presence of surfactant.

[44] Not surprisingly, we find that the structure of wakes around vegetation stems affects surface divergence and that the structure of these wakes depends on the wind forcing conditions. Surveying the flow around a variety of different stems while <U_{canopy}> ≈ 1 m s^{−1}, we find the following approximate surface divergence behavior:

[45] There is a region of enhanced surface divergence surrounding each stem, with a diameter roughly twice that of the stem diameter.

[46] In this region of enhanced surface divergence, on average, |γ_{wake}|^{1/2} ≈ 1.2 s^{−1/2}.

[47] Far from the stems, on average, |γ_{background}|^{1/2} ≈ 0.50 s^{−1/2}.

[48] Combining these observations with a Monte Carlo analysis that predicts the amount of water surface covered in wakes, we can estimate an areal average |γ|^{1/2}. For the plant volume fraction ϕ = 2% used in our experiments, this gives |γ|^{1/2} = 0.54 s^{−1/2}. Using this value in equation (11) gives k_{600} = 1.4 cm h^{−1} for n = 2/3, which falls inside the confidence interval of the lowest k_{600} values we measured by monitoring DO increase at <U_{canopy}> ≈ 1 m s^{−1}. The agreement between these independent measurements serves as a check of our methodology. For <U_{canopy}> ≈ 0.2 m s^{−1}, the surface divergence is reduced, particularly near the stems. Unlike the high wind speed case, only the slightest increase in surface divergence above background is visible near stems (e.g., Figure 7 inset).

[49] Combining our approximate surface divergence data for <U_{canopy}> ≈ 1 m s^{−1}, the Monte Carlo model for wake area fraction, and the surface divergence model for k, we can predict how k varies with plant volume fraction at this wind speed. For the same <U_{canopy}> and stem diameter, k varies almost linearly with ϕ over the common range of plant volume fractions. For n = 2/3, the slope is 0.06 cm h^{−1} per percentage point increase in plant volume fraction. This suggests that k_{600} will be essentially the same over the range of ϕ observed in S. acutus and S. californicus marshes (0.01–0.04), in cases where <U_{canopy}> ≈ 1 m s^{−1}. At lower <U_{canopy}> values, wind plays a role in gas transfer subordinate to thermal convection, and thermal convection is unlikely to be affected by plant volume fraction for ϕ less than 0.06. That k is largely insensitive to ϕ at <U_{canopy}> ≈ 1 m s^{−1} can be attributed to the small size of the high-divergence region around each stem. This suggests that the regions of enhanced stirring in plant wakes play a minor role in gas transfer, at least in the presence of surfactants. We cannot rule out a greater role for wakes (and increased variability of k with ϕ) when surfactants are absent or for larger-diameter plants, which would produce larger wakes at the same wind speed.

5.6 Comparison With Gas Transfer Models and Data From Lakes

[50] In Figure 8, we plot our results along with data and models for k_{600} from the literature. The models were derived from measurements of k_{600} in lakes [MacIntyre et al., 2010; Cole and Caraco, 1998]; the points represent individual measurements made in a wetland pond free of emergent vegetation [Sebacher et al., 1983]. On the x axis in the plot is the wind speed at a height of 0.4 m above the water surface, the height at which we measured <U_{canopy}> in our measurements of k_{600} in the laboratory. MacIntyre et al. [2010] and Cole and Caraco [1998] report wind speed 10 m above the water surface, while Sebacher et al. [1983] measured wind speeds 2 cm above the water surface. We scaled these wind speeds to a height of 0.4 m above the water surface using a typical value for the roughness height over open water.

[51] The regression of MacIntyre et al. [2010] for q > 0 and to a lesser extent the model of Cole and Caraco [1998] fit our laboratory data collected while <U_{canopy}> exceeded 0.7 m s^{−1}. The k_{600} value we measured for q = −310 W m^{−2}, however, falls closer to the MacIntyre et al. [2010] regression for q < 0. We surmise that compared to wetlands with emergent vegetation, surface heat fluxes in lakes are more often in the range of q < −300 W m^{−2}, resulting in generally higher gas transfer velocities during periods of surface cooling. The wetland pond k_{600} measurement at a wind speed of 0.8 m s^{−1} by Sebacher et al. [1983] overlaps with our laboratory data; their measurement at zero wind speed does not. Empirical relationships derived in lakes and ponds may be sufficient for predicting gas transfer for high in-canopy wind speeds in wetlands with emergent vegetation if in-canopy wind speed is known. For in-canopy wind speeds less than 0.7 m s^{−1}, there was no discernible, monotonic trend in the laboratory data with wind speed and it is preferable to model k_{600} as a function of heat loss.

6 Conclusions

[52] We have used laboratory experiments to examine the relationship between interfacial gas flux and stirring by wind and thermal convection in wetlands with emergent vegetation. The experimental settings are based on field measurements in a Northern California marsh with an emergent plant canopy of Typha spp. and S. acutus, as well as data from similar wetlands in the literature. At in-canopy wind speeds equal to those measured in the field, gas transfer velocities in the model wetland were largely insensitive to in-canopy wind speed. Instead, thermal convection induced by heat loss at the water surface appeared to drive most hydrodynamic gas transfer. We saw evidence for this in the agreement between gas transfer velocities measured in the model wetland and gas transfer velocities predicted from a semiempirical function of surface heat loss. For mean in-canopy wind speeds greater than those observed in the field, measured gas transfer velocities increased with increasing wind speed and exceeded those predicted to occur due to thermal convection alone. Based on these results, we infer a quadratic relationship between mean in-canopy wind speed and gas transfer velocity. Because of the high turbulent intensities observed in the wetland canopy in the field, an enhancement factor must be included in this relationship.

[53] Particle image velocimetry revealed regions of increased surface divergence, and hence increased air-water gas transfer, around emergent plant stems. With surfactants present, the combined area of these high-divergence regions is small, suggesting that variations in the density of plant stems do not directly affect wetland air-water gas transfer, and that the predominant effect of emergent stems on wind-driven gas transfer is the attenuation of the wind speed above the water surface. Indeed, k values measured in the model wetland at high in-canopy wind speed correspond with k values predicted by some empirical relationships for lakes once the wind speed in these relationships is scaled to a height below the canopy height.

[54] Regular nightly increases in k due to thermal convection are strong enough to make hydrodynamic gas transfer a significant component of the biogeochemical budget in wetlands with emergent vegetation. Air-water oxygen flux, assuming a reasonable value for the wetland water column dissolved oxygen and the surface heat loss, is likely of the same magnitude as plant-mediated oxygen flux. In addition, high in-canopy wind speeds, though rare, could cause spikes in air-water gas fluxes that contribute sizably to overall gas transfer. The predictive models for gas transfer velocity that we have identified can be used to approximate interfacial gas fluxes over a range of wind speeds and surface heat fluxes. Applications include partitioning eddy covariance measurements of net gas flux by transport pathway and more accurately representing gas transport in wetland biogeochemical models.

Acknowledgments

[55] We thank UC Berkeley students Raymond Wong, Oliver Rickard, Bill Chen, and Heidi Chou for their contributions to model construction and data collection and analysis. Thanks also to Robin Miller, Frank Anderson, Bryan Downing, Robert Fujii, and Lisamarie Windham-Myers of the USGS for Twitchell Island wetlands information and access. Four anonymous reviewers provided excellent suggestions for improving the manuscript.